What is 1.2*5^{(-3/2)} ?

The solution to 1.2*5^{(-3/2)} is 6/(25*5^{1/2)}

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simplify 1.2*5^{(-3/2)}

simplify

1.2 \cdot 5^{(- \frac{3}{2})}

\frac{6}{25 \cdot 5 ^{\frac{1}{2}}}

Decimal Notation

0.10733 \dots

Solution steps

1.2 \cdot 5^{- \frac{3}{2}}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

5^{- \frac{3}{2}} = \frac{1}{5 ^{\frac{3}{2}}}

= 1.2 \cdot \frac{1}{5 ^{\frac{3}{2}}}

5^{\frac{3}{2}} = 5 \cdot 5^{\frac{1}{2}}

= 1.2 \cdot \frac{1}{5 \cdot 5 ^{\frac{1}{2}}}

1.2 \cdot \frac{1}{5 \cdot 5 ^{\frac{1}{2}}} = \frac{1.2}{5 ^{\frac{1}{2}} \cdot 5}

= \frac{1.2}{5 ^{\frac{1}{2}} \cdot 5}

\frac{1.2}{5 ^{\frac{1}{2}} \cdot 5} = \frac{12}{50 \cdot 5 ^{\frac{1}{2}}}

= \frac{12}{50 \cdot 5 ^{\frac{1}{2}}}

Factor the number:

12 = 2 \cdot 6

= \frac{2 \cdot 6}{50 \cdot 5 ^{\frac{1}{2}}}

Factor the number:

50 = 2 \cdot 25

= \frac{2 \cdot 6}{2 \cdot 25 \cdot 5 ^{\frac{1}{2}}}

Cancel the common factor:

2

= \frac{6}{25 \cdot 5 ^{\frac{1}{2}}}

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